Question

A baseball player (Fig. 5-31) with mass \(79 \mathrm{~kg}\), sliding into a base, is slowed by a force of friction of \(470 \mathrm{~N}\). What is the coefficient of kinetic friction between the player and the ground?

Short answer

The coefficient of kinetic friction between the player and the ground is approximately 0.61.

Step-by-step solution

Calculate the normal force (Fn)

The normal force (Fn) is the weight of the baseball player which can be calculated by multiplying mass with gravity. Here, the mass is \(79 \mathrm{~kg}\) and gravity is \(9.8 \mathrm{~m/s^2}\). So, \(Fn = mass \times gravity = 79 \mathrm{~kg} \times 9.8 \mathrm{~m/s^2} = 774.2 \mathrm{~N}\)

Calculate the coefficient of kinetic friction

Now the coefficient of kinetic friction can be calculated with the formula \(\mu = F_f / F_n \), where the frictional force \(F_f\) is given as \(470 \mathrm{~N}\). So, \(\mu = 470 \mathrm{~N} / 774.2 \mathrm{~N} = 0.6072\)

Key concepts

Normal Force

The normal force is a vital concept in understanding how objects interact with surfaces. It is essentially the support force exerted by a surface, perpendicular to the surface. When an object is placed on a flat surface, the normal force balances the object's weight due to gravity, keeping it stationary.In our baseball player scenario, the normal force acts upwards, counteracting the player's weight. To compute this, we multiply the player's mass by the acceleration due to gravity. Given:

• Mass of player: 79 kg
• Gravity: 9.8 m/s²

The normal force (Fn) is calculated as:\[ F_n = \text{mass} \times \text{gravity} = 79 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 774.2 \, \text{N} \]This tells us that the force pushing up against the player, due to the ground, is 774.2 N. Understanding normal force is crucial as it is a key player in calculating friction.

Force of Friction

Friction is the force resisting the relative motion of surfaces sliding past each other. It is critical to many everyday activities such as walking or driving. There are two main types of friction: static and kinetic. Our focus here is kinetic friction because our baseball player is sliding. The force of friction ( F_f ) acts opposite to the direction of motion. In this exercise, friction slows the player down as they slide into the base. It is given as 470 N. Kinetic friction is dependent on:

• The normal force
• The coefficient of kinetic friction

Together, they determine how much the surface impedes motion. Remember, while friction can slow things down, it is also essential for controlling movement which is incredibly helpful in various sports and applications.

Coefficient of Friction

The coefficient of kinetic friction (\mu_k) is a dimensionless number that represents how easily one surface slides over another. It varies depending on the textures and materials involved.Calculating \mu_k is straightforward once the normal force and the frictional force are known. The formula is:\[ \mu_k = \frac{F_f}{F_n} \]Substituting the values from our baseball scenario:

• Frictional force (F_f): 470 N
• Normal force (F_n): 774.2 N

We find:\[ \mu_k = \frac{470 \, \text{N}}{774.2 \, \text{N}} \approx 0.6072 \]This tells us that the surfaces (player and ground) aren’t perfectly smooth, indicating a moderate level of friction. By understanding \mu_k, you can predict how different surfaces will interact under similar conditions.